System and method for electromagnet coil construction and operation

ABSTRACT

A method of manufacturing electromagnet coils for use in a magnetic resonance imaging (MRI) system is provided. The method comprises forming a coil representation of a coil surface for the electromagnet coils; setting a plurality of performance metric requirements for a plurality of performance metrics for the electromagnet coils, the plurality of performance metrics including a magnetic field-shape metric and an eddy-field metric; forming a performance functional, based on the coil representation and the plurality of performance metrics, for generating a current density pattern over the coil surface; optimizing the performance functional based on the plurality of performance metric requirements; generating a current density pattern over the coil surface based on the minimized performance functional; and obtaining coil windings from the current density pattern.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.14/894,212 filed Nov. 25, 2015, which is a 371 of International PatentApplication No. PCT/CA2014/000874 filed Dec. 9, 2014. The content ofthese patent applications is hereby expressly incorporated by referenceinto the detailed description hereof.

FIELD OF THE INVENTION

The present invention relates generally to magnetic resonance imaging.More specifically, the present invention relates to the construction andoperation of electromagnetic coils.

BACKGROUND OF THE INVENTION

Magnetic resonance imaging (MRI) is a major imaging technique used inmedicine. MRI is capable of generating detailed images of soft tissuessuch as the brain, muscles and kidneys. Specific properties of thevarious compounds found inside tissues, such as water and/or fat, areused to generate images. When subjected to a strong magnetic field, thevector sum of the nuclear magnetic moments of a large number of atomspossessing a nuclear spin angular momentum, such as hydrogen, which isabundant in water and fat, will produce a net magnetic moment inalignment with the externally applied field. The resultant net magneticmoment can furthermore precess with a well-defined frequency that isproportional to the applied magnetic field. After excitation by radiofrequency pulses, the net magnetization will generate a signal that canbe detected.

Various electromagnets are integral parts of an MRI system. They allowthe generation of the main magnetic field, the spatial encoding of thedetected signals for the formation of spatial images, and correction ofany irregularities. Electromagnets perform this function by generatingmagnetic fields with predetermined shapes. For example, the main magnetis designed to generate a magnetic field that is as uniform as possible,across all dimensions. Gradient coils on the other hand are designed togenerate magnetic fields that vary linearly with a constant tangentalong the three perpendicular axis of the MRI systems' imaging volume.

Manufacturing electromagnets which can generate magnetic fields with thedesired requirements such as magnetic field shapes can presentchallenges. Specifically, to function properly, electromagnets aretypically produced to operate in accordance with additional requirementsbesides magnetic field shape. For example, it is desirable to producegradient coils, which when energized produce minimal eddy fields. Thisrequirement is in addition to the linearity of the magnetic fieldproduced. However, when the gradient coils are asymmetric in thelongitudinal direction (z), for example, eddy fields and net torque andforce can be generated which can disrupt the operation of an MRI system.Thus, improved electro-magnet manufacturing and operating techniques areneeded to allow the construction of electro-magnets that better meetdesired requirements while being able to generate magnetic fields thatcorrespond to a desired field shape.

SUMMARY OF THE INVENTION

It is an object to provide a novel system and method for an MRI scanningsystem and method that obviates and mitigates at least one of theabove-identified disadvantages of the prior art.

According to one aspect, a method of manufacturing electromagnet coilsfor use in a magnetic resonance imaging (MRI) system is provided. Themethod comprises forming a coil representation of a coil surface for theelectromagnet coils; setting a plurality of performance metricrequirements for a plurality of performance metrics for theelectromagnet coils, the plurality of performance metrics including amagnetic field-shape metric and an eddy-field metric; forming aperformance functional, based on the coil representation and theplurality of performance metrics, for generating a current densitypattern over the coil surface; optimizing the performance functionalbased on the plurality of performance metric requirements; generating acurrent density pattern over the coil surface based on the minimizedperformance functional; and obtaining coil windings from the currentdensity pattern.

These, together with other aspects and advantages which will besubsequently apparent, reside in the details of construction andoperation as more fully hereinafter described and claimed, referencebeing had to the accompanying drawings forming a part hereof, whereinlike numerals refer to like parts throughout.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a block diagram of functional subsystems of a magneticresonance imaging system in accordance with an implementation;

FIG. 2 shows an imaging volume and corresponding slice to be scanned bythe magnetic resonance system of FIG. 1 in accordance with animplementation;

FIG. 3 shows an example pulse sequence in accordance with animplementation;

FIG. 4 shows a schematic representation of a k-space containing onereceived line in accordance with an implementation;

FIG. 5 shows a gradient coil wire pattern that is asymmetric along thelongitudinal direction with one spiral per layer in accordance with animplementation.

FIG. 6 shows an example linear eddy field profile (a) and itscompensated form (b) in accordance with an implementation;

FIG. 7 shows an example non-linear eddy field profile in accordance withan implementation;

FIG. 8 shows an example digitized cylindrical surface in accordance withan implementation;

FIG. 9 shows the example digitized cylindrical surface with a streamfunction pattern and a corresponding coil wire pattern in accordancewith an implementation; and

FIG. 10 shows a flowchart for a method of manufacturing gradient coilsfor use in the magnetic resonance imaging system of FIG. 1 in accordancewith an implementation.

DETAILED DESCRIPTION

Referring to FIG. 1, a block diagram of a magnetic resonance imaging(MRI) system, in accordance with an example implementation, is shown at100. The example implementation of the MRI system indicated at 100 isfor illustrative purposes only, and variations including additional,fewer and/or varied components are possible. Traditional magneticresonance imaging (MRI) systems represent an imaging modality which isprimarily used to construct pictures of magnetic resonance (MR) signalsfrom protons such as hydrogen atoms in an object. In medical MRI,typical signals of interest are MR signals from water and fat, the majorhydrogen containing components of tissues.As shown in FIG. 1, the illustrative MRI system 100 comprises a dataprocessing system 105. The data processing system 105 can generallyinclude one or more output devices such as a display, one or more inputdevices such as a keyboard and a mouse as well as one or more processorsconnected to a memory having volatile and persistent components. Thedata processing system 105 can further comprise one or more interfacesadapted for communication and data exchange with the hardware componentsof MRI system 100 used for performing a scan.Continuing with FIG. 1, the example MRI system 100 can also include amain field magnet 110. The main field magnet 110 can be implemented as apermanent, superconducting or a resistive magnet, for example. Othermagnet types, including hybrid magnets suitable for use in the MRIsystem 100 will now occur to a person of skill and are contemplated. Themain field magnet 110 is operable to produce a substantially uniformmain magnetic field having a strength B0 and a direction along an axis.The main magnetic field is used to create an imaging volume within whichdesired atomic nuclei, such as the protons in Hydrogen within water andfat, of an object are magnetically aligned in preparation for a scan. Insome implementations, as in this example implementation, a main fieldcontrol unit 115 in communication with data processing system 105 can beused for controlling the operation of the main field magnet 110.The MRI system 100 can further include gradient coils, for examplegradient coils 120 used for encoding spatial information in the mainmagnetic field along, for example, three perpendicular gradient axes.The size and configuration of the gradient coils 120 can be such thatthey produce a controlled and uniform linear gradient. For example,three paired orthogonal current-carrying primary coils located withinthe main field magnet 110 can be constructed to produce desiredlinear-gradient magnetic fields.In some implementations, the gradient coils 120 may be shielded andinclude an outer layer of shield magnets, for example coils, which canproduce a counter magnetic field to counter the gradient magnetic fieldproduced by the primary gradient coils forming a primary-shield coilspair. In such a coil pair the “primary” coils can be responsible forcreating the gradient field and the “shield” coils can be responsiblefor reducing the stray field of the primary coil outside a certainvolume such as those external to the gradient coils 120. Theprimary-shield coils pair of the gradient coils 120, the primary andshield coils, may be connected in series. It is also possible to havemore than two layers of coils for any given gradient axis that togetherform shielded gradient coils 120. The shielded gradient coils 120 mayreduce eddy currents and other interference which can cause artefacts inthe scanned images. Since eddy currents mainly flow in conductingcomponents of the MRI system 100 and are caused by time-varying magneticfields external to the gradient coils 120 (leakage fields), reducing theleakage fields produced by the gradient coils 120 may reduceinterference. Accordingly, the shapes and sizes, conductor wire patternsand sizes, and current amplitudes and patterns of the primary-shieldcoils pair can be selected so that the net magnetic field outside thegradient coils 120 is as close to zero as possible. For cylindricalmagnets, for example, the two coils can be arranged in the form ofconcentric cylinders whereas for vertical field magnets, the two coilsmay be arranged in coaxial disks.One side effect of shielding can be that the fields produced by theprimary-shield coils pair of the gradient coils 120 may partially canceleach other within the imaging volume. Accordingly, more current can berequired to produce a gradient field with a particular strength byshielded gradient coils 120 than by unshielded gradient coils 120. Thiseffect can be quantified as the gradient efficiency, which may bedefined as the achievable gradient strength for 1 Ampere of drivingcurrent. Another important parameter describing gradient coilperformance is called the gradient slew rate, which is the rate ofdriving a gradient coil from zero to its maximum amplitude. The maximumachievable slew rate is lower in gradient coils with greater inductancewhen driven with the same power amplifier. Typically, in order toincrease the efficiency of a shielded gradient coils 120 to becomparable to the efficiency of an unshielded gradient coils 120 theinductance must increase. This increase in inductance will decrease themaximum achievable slew rate. The loss in efficiency for a shieldedconfiguration can depend on the distance and current density ratiobetween the primary and shield coils. Increasing the distance betweenthe primary-shield coils pair may increase the efficiency.The conductive components of the gradient coils 120, whether shielded orunshielded and including the primary and shield coils, may consist of anelectrical conductor (for example copper, aluminum, etc.). The internalelectrical connections can be such that when a voltage difference isapplied to the terminals of the gradient coils 120, electric current canflow in the desired path. The conductive components for the threegradient axes for both the primary gradient coils and the gradientshield coils can be insulated by physical separation and/or anon-conductive barrier. The primary gradient windings can be placed on anon-conductive substrate (for example, G10, FR4, epoxy or others).In some variations, the gradient coils 120 may also be provided withthermal control or heat extraction mechanisms. For example, some of thewindings can be hollow and coolant can be passed through these hollowconductors to extract heat from the gradient coils 120, produced, forinstance, by resistive heating of the windings when electricity isapplied. Alternatively, other methods of extracting heat can be used,such as inserting coolant channels within the gradient coils 120. Thecoolant channels can be in thermal contact with the gradient coilwindings. The gradient coils 120 can also be mounted in athermally-conductive but electrically-non-conductive epoxy to ensurethat the mechanical assembly is rigid and to limit the possibility ofelectrical breakdown.The magnetic fields produced by the gradient coils 120, in combinationand/or sequentially, can be superimposed on the main magnetic field suchthat selective spatial excitation of objects within the imaging volumecan occur. In addition to allowing spatial excitation, the gradientcoils 120 can attach spatially specific frequency and phase informationto the atomic nuclei placed within the imaging volume, allowing theresultant MR signal to be reconstructed into a useful image. A gradientcoil control unit 125 in communication with the data processing system105 can be used to control the operation of the gradient coils 120.In some implementations of the MRI system 100, there may be additionalelectromagnet coils present, such as correction coils 140. Thecorrection coils 140, which can include shim coils, a uniform fieldoffset coil and any other corrective electromagnets, traditionallyproduce (but are not limited to) magnetic field profiles of 2nd order orhigher spherical harmonics or uniform magnetic fields. To perform activecorrection or shimming (correcting the field distortions that areintroduced when different objects are placed within or around thesystem), the corrective electromagnets, such as the correction coils140, carry a current that is used to provide magnetic fields that act tomake the main magnetic field more uniform. For example, the fieldsproduced by these coils can aid in the correction of inhomogeneities inthe main magnetic field due to imperfections in the main magnet 110, orto the presence of external ferromagnetic objects, or due tosusceptibility differences of materials within the imaging region, orany other static or time-varying phenomena. A correction coil controlunit 140 in communication with the data processing system 105 can beused to control the operation of the shim coils 140.The MRI system 100 can further comprise radio frequency (RF) coils 130.The RF coils 130 are used to establish an RF magnetic field with astrength B1 to excite the atomic nuclei or “spins”. The RF coils 130 canalso detect signals emitted from the “relaxing” spins within the objectbeing imaged. Accordingly, the RF coils 130 can be in the form ofseparate transmit and receive coils or a combined transmit and receivecoil with a switching mechanism for switching between transmit andreceive modes.The RF coils 130 can be implemented as surface coils, which aretypically receive only coils and/or volume coils which can be receiveand transmit coils. The RF coils 130 can be integrated near the mainfield magnet 110 bore. Alternatively, the RF coils 130 can beimplemented in closer proximity to the object to be scanned, such as ahead, and can take a shape that approximates the shape of the object,such as a close-fitting helmet. An RF coil control unit 135 incommunication with the data processing system 100 can be used to controlthe operation of the RF coils 130.There are many techniques for obtaining images using the MRI system 100,including T1 and T2 weighted images. To provide a simplifiedillustration of the MRI system 100's functionality, simplifiedoperations for obtaining proton density-weighted images are described asa non-limiting example. To create an image in accordance with theexample illustration, the MRI system 100 detects the presence of atomicnuclei containing spin angular momentum in an object, such as those ofHydrogen protons in water or fat found in tissues, by subjecting theobject to a relatively large magnetic field. In this exampleimplementation, the main magnetic field has a strength of B0 and theatomic nuclei containing spin angular momentum may be Hydrogen protonsor simply protons. The main magnetic field partially polarizes theHydrogen protons in the object placed in the imaging volume of the mainmagnet 110. The protons are then excited with appropriately tuned RFradiation, forming an RF magnetic field with a strength of B1, forexample. Finally, weak RF radiation signal from the excited protons isdetected as an MR signal, as the protons “relax” from the magneticinteraction. The frequency of the detected MR signal is proportional tothe magnetic field to which they are subjected. Cross-sections of theobject from which to obtain signals can be selected by producing amagnetic field gradient across the object so that magnetic field valuesof the main magnetic field can be varied along various locations in theobject. Given that the signal frequency is proportional to the variedmagnetic field created, the variations allow assigning a particularsignal frequency and phase to a location in the object. Accordingly,sufficient information can be found in the obtained MR signals toconstruct a map of the object in terms of proton presence, which is thebasis of a traditional MRI image. For example, since proton densityvaries with the type of tissue, tissue variations can be mapped as imagecontrast variations after the obtained signals are processed.Referring now to FIG. 2, to further illustrate the example signalacquisition process by the MRI system 100, it will be assumed that anobject is placed within an imaging volume 250 of the main magnet 110having a main magnetic field 210 with a strength B0, pointing along theZ-axis indicated at 240. The object subsequently has a net magnetizationvector. In this illustrative example, a slice in a plane along the X andY axes, as indicated at 205, is being imaged. It should be noted that inthis example, the slice has a finite thickness along the Z-axis,creating a volumetric slice 205.To obtain images from the MRI system 100 in the traditional manner, oneor more sets of RF pulses and gradient waveforms (collectively called“pulse sequences”) are selected at the data processing system 105. Thedata processing system 105 passes the selected pulse sequenceinformation to the RF control unit 135 and the gradient control unit125, which collectively generate the associated waveforms and timingsfor providing a sequence of pulses to perform a scan.The sequence of RF pulses and gradient waveforms, namely the type ofpulse sequence, applied may change which relaxation times have the mostinfluence on the image characteristics. For example, T2* relaxation hasa significant influence following a 90° RF pulse which is used in agradient-echo (GRE) sequence, whereas T2 relaxation has a moresignificant influence following 90°-180° sequential RF pulses (alsoknown as a spin echo sequence).Referring now to FIG. 3, an illustrative pulse sequence 300 is shownthat can be used to acquire images using the MRI system 100.Specifically, a timing diagram for the example pulse sequence isindicated. The timing diagram shows pulse or signal magnitudes, as afunction of time, for the transmitted (RFt) signal, the magnetic fieldgradients G_(x), G_(y), and G_(z), and the received RFx signal. Anidealized pulse sequence, simplified for illustrative purposes, cancontain a slice selection radio frequency pulse 310 at RFt, a sliceselection gradient pulse 320 at Gz, a phase encoding gradient pulse 330at Gy, a frequency encoding gradient pulse 340 at Gx, as well as adetected MR signal 350 at RFx. The pulses for the three gradients Gx,Gy, and Gz represent the magnitude and the duration of the magneticfield gradients that can be generated by the gradient coils 120. Theslice selection pulse 310 can be generated by the transmit aspect of RFcoils 130. The detected MR signal 350 can be detected by the receiveaspect of the RF coils 130. In this illustrative example it will beassumed that the transmit aspect and the receive aspect of the RF coils130 are formed by distinct coils.The first event to occur in pulse sequence 300 can be to turn on theslice selection gradient pulse 320. The slice selection RF pulse 310 canbe applied at the same time. In this illustrative example, the sliceselection RF pulse 310 can be a sinc function shaped burst of RF energy.In other implementations, other RF pulse shapes and durations can beused. Once the slice selection RF pulse 310 is turned off, the sliceselection gradient pulse 320 can also be turned off and a phase encodinggradient pulse 330 can be turned on. Once the phase encoding gradientpulse 330 is turned off, the frequency encoding gradient pulse 340 canbe turned on and the detected MR signal 350 can be recorded. It shouldbe noted that the shapes, magnitudes, ordering and durations of thepulses and signals shown in FIG. 3 are chosen for illustrative purposes,and that in implementations, one or more of these factors and others maybe varied to achieve the desired scan results.The pulse sequence 300 can be repeated a certain number of times oriterations, for example 256 times, to collect all the data needed toproduce one image. The time between each repetition of the pulsesequence 300 can be referred to as the repetition time (TR). Moreover,the duration between the center point of the slice selection pulse 310and the peak of detected MR signal 350 can be referred to as echo time(TE). Both the TR and the TE can be varied as appropriate for a desiredscan.To further illustrate the signal acquisition process of MRI system 100,FIG. 2 is referred to in conjunction with FIG. 3. To select a slice, theslice selection gradient pulse 320 can be applied along the Z-axis,satisfying the resonance condition for the protons located in the slice205. Indeed, the location of the slice along the Z-axis can bedetermined based in part on the slice selective gradient pulse 320.Accordingly, the slice selection pulse 310, generated at the same timeas the slice selection gradient pulse 320 can excite protons that arelocated within the slice 205 in this example. Protons located above andbelow the slice 205 are typically not affected by the slice selectionpulse 310.Continuing with the illustrative example, in accordance with the pulsesequence 300, a phase encoding gradient pulse 330 can be applied afterthe slice selection gradient pulse 320. Assuming this is applied alongthe Y-axis, the spins at different locations along the Y-axis can beginto precess at different Larmor frequencies. When the phase encodinggradient pulse 330 is turned off, the net magnetization vectors atdifferent locations can precess at the same rate, but possess differentphases. The phases can be determined by the duration and magnitude ofthe phase encoding gradient pulse 330.Once the phase encoding gradient pulse 330 is turned off, a frequencyencoding gradient pulse 340 can be turned on. In this example thefrequency encoding gradient is in the X direction. The frequencyencoding gradient can cause protons in the selected slice to precess atrates dependent on their X location. Accordingly, different spatiallocations within the slice are now characterized by unique phase anglesand precessional frequencies. RF receive coils 130 can be used toreceive the detected signal 350 generated by the protons contained inthe object being scanned while the frequency encoding gradient pulse 340is turned on.As the pulse sequence 300 is performed by the MRI system 100, theacquired signals can be stored in a temporary matrix referred to as thek-space, as shown in FIG. 4 at 400. Typically, the k-space is thecollection of the detected signals measured for a scan and is in thespatial frequency domain. The k-space can be covered by frequencyencoding data along the X-axis 420 (Kx) and phase encoding data alongthe Y-axis 430 (Ky). When all of the lines for the k-space matrix for aslice are received (at the end of the scan of a single slice, forexample) the data can be mathematically processed, for example through atwo-dimensional Fourier-transform, to produce a final image. Thus, thek-space can hold raw data before reconstruction of the image into thespatial domain. Typically, the k-space has the same number of rows andcolumns as the final image and is filled with raw data during the scan,usually one line per pulse sequence 300. For example, the first line ofthe k-space 400, indicated at 410, is filled after the completion of thefirst iteration of the pulse sequence generated for scanning a slice andcontains the detected signal for that pulse sequence iteration. Aftermultiple iterations of the pulse sequence, the k-space can be filled.Each iteration of the pulse sequence may be varied slightly, so thatsignals for the appropriate portions of the k-space are acquired. Itshould be noted that based on different pulse sequences, other methodsof filling the k-space are possible, such as in a spiral manner, and arecontemplated.The gradient coils 120 produce time-varying magnetic fields with aspecific spatial distribution and are a typical component of MRIsystems. Greater field-variation magnitudes enable faster MR imagingsequences and increased resolution. As discussed above, the maximumachievable gradient strength is characterized by the gradientefficiency. The efficiency of the gradient coils 120 can be improvedthrough variations in the shape, size and placement of the gradientcoils 120. For example, in a cylindrical implementation the primarygradient coil windings may be built at a smaller radius closer to theobject in the imaging volume. Alternatively, the number of wires(winding density) can be increased.

The gradient coils 120 can have a high degree of symmetry when, forexample, the object to be imaged is located at the center of the coils.Accordingly, such coils are typically referred to as symmetric gradientcoils. Due to physical and geometrical constraints, for some MRI systems100, the objects to be imaged may not be located symmetrically at thecenter of the gradient coils 120. Further, such coils may not even besymmetric in shape. For example, a head gradient coil may fit the head,but not the shoulders. Alternatively, there may be slots for shoulderswith the coil extending above the chest and underneath the back. Coilsof this type are typically known as asymmetric gradient coils.

When the gradient coils 120 are constructed, certain performance metricscan be considered. For example, the gradient coils 120 are typicallyconstructed so as to reduce net force and torque experienced when theyare energized. Net force can be characterized in each of the x, y and zdirections in terms of Newtons per Ampere of current and this quantitydetermines the tendency for the coil to translate in space whenenergized. Net torque can be characterized in each of the x, y and zdirections in terms of Newtons per meter per Ampere and this quantitydetermines the tendency for the coil to rotate when energized. Achievingforce- and torque-balance is a particularly challenging problem forgradient coils 120 that are asymmetric along the longitudinal (z)dimension. For example, as shown in FIG. 5, gradient coils that areasymmetric along the longitudinal direction can have wire patterns withsingle spirals 510 (hereafter referred to as ‘thumbprint’ 510) for eachside of the coil, an arrangement that can enable increased efficiency.In this example, two additional thumbprints 510′ are shown which are theportions of the shield coil corresponding to the primary coil.

The gradient coils 120 are typically designed and constructed to lowernet force and torque from such asymmetric designs. For example, in somevariations, a shield coil can be used to cancel the torque of a primarycoil when the two coils are part of the same rigid mechanical assembly.When the primary and the shield coil wire patterns form part of the samerigid mechanism, it is possible to get torque-balanced implementationsby using a single thumbprint for the primary coil and a singlethumbprint for the shield coil, although it can also be possible toachieve torque-balanced implementations for other patterns and numbersof thumbprints. Other considerations such as wire density and patterncan also be used to reduce net torque and force. The reduction in nettorque and force experienced is made in consideration of otherperformance metrics limits. Thus, in some implementations, optimum forceand torque-balance may be sacrificed to achieve requirements set forother performance metrics.

Efficiency is another performance metric to be considered whenconstructing the gradient coils 120. Efficiency can be defined as thegradient strength per unit current driven through the gradient coils120. High efficiency aids the production of large gradient amplitudes,which in turn can allow the acquisition of higher resolution images orreduce scan times for example. Efficiency is linearly proportional tothe winding density of the gradient coils 120. For example, when thewinding density is doubled, the efficiency typically doubles as well.Accordingly, the gradient coils 120 are typically constructed with ashigh an efficiency as possible, in light of other performance metrics,including requirements set for other performance metrics. Thus, in someimplementations, optimum efficiency may be sacrificed to achieverequirements set for other performance metrics. For example, aparticular winding density can be chosen to obtain a desired efficiencythat may be lower than the highest possible efficiency so that limitsfor other performance metrics can be met.

Power dissipation is yet another performance metric to be considered.Power dissipation can be determined based on power which is theresistance of the gradient coils 120 multiplied by the current squared.Accordingly, power dissipation can be a measure of the amount of heatthat can be created when the gradient coils 120 are energized. Powerdissipation is proportional to the square of the winding density. Forexample, when the winding density is doubled, the power dissipationtypically quadruples. Accordingly, the gradient coils 120 are typicallyconstructed with as low a power dissipation (and thus heat generation)as possible, in light of other performance metric requirements set. Forexample, a particular winding density can be chosen to obtain a desiredpower dissipation that may be higher than the lowest possible powerdissipation so that requirements set for other performance metrics canbe met.

Energy is a further performance metric that can be considered whenconstructing the gradient coils 120. Energy can be defined as theinductance of the gradient coils 120 multiplied by the current squaredmultiplied by 0.5. This metric can be a measure of how fast the gradientcoils 120 can be switched on or off. Lower energy typically impliesfaster switching rates. Energy, similar to power dissipation isproportional with the square of the winding density. For example, whenthe winding density is doubled, the energy typically quadruples.Accordingly, the gradient coils 120 are typically constructed with aslow an energy (fastest switching) as possible, in light of otherperformance metric requirements. For example, a particular windingdensity can be chosen to obtain a desired energy that may be higher thanthe lowest possible energy so that the requirements set for otherperformance metrics can be met.

Gradient field-shape metric is a further performance metric. Magneticfield gradient linearity and uniformity is typically a primaryconsideration when implementing the gradient coils 120. Gradientfield-shape metric is a measure of how well the field that the gradientcoils 120 produces matches a target gradient field, which in the exampleMRI system 100 has a linear and uniform spatial gradient. There are manyways that this gradient metric can be defined. An example definition isthe sum of the squared difference between the field that is produced bythe gradient coils 120 and the target gradient field over a set ofpositions in a volume of interest. Based on this definition, thegradient field-shape metric is lowered, to the extent possible, in lightof other performance metric requirements specified. For example, aparticular winding pattern can be chosen to obtain a particular gradientlinearity metric that may be higher than the lowest possible gradientlinearity metric so that specified requirements for other performancemetrics can be met.

Another performance metric of interest is the eddy-field metric. Eddycurrents are induced on conducting surfaces other than the energizedgradient coils 120, such as within the main magnet 110 bore. Asdiscussed above, the unshielded gradient coils 120 may producetime-varying magnetic fields outside the gradient coils 120. Thesefields may induce eddy currents in external conducting surfaces outsideof the gradient coil, such as the cylindrical main magnet 110 bore. Asfurther discussed above, eddy currents can create undesirabletime-varying magnetic fields (eddy fields) within the imaging volume andcan adversely affect image quality for many imaging sequences. Themagnitude of eddy field effects can be greatly reduced by the additionof gradient shield coils, which typically consist of opposite sensewindings outside of the primary gradient coils.

Although the magnitude of eddy currents induced by the shielded gradientcoils 120 is substantially reduced compared to the unshielded gradientcoils 120, eddy currents are not completely eliminated by the use ofshield gradient coils 120. Indeed, some eddy fields remain despite theshielding. Where the gradient coils 120 are symmetric and shielded, andthe conducting surface is symmetric with respect to the gradient coil,the spatial field profile of the eddy fields typically match the spatialfield profile of the magnetic field generated by gradient coils 120.Namely, they may have substantially spatially linear profiles, as shownin FIG. 6(a) for example. The eddy fields may thus be compensated for byminor adjustments to the current waveform sent through the gradientcoils 120 as shown in FIG. 6(b).

In the case of asymmetric shielded gradient coils 120, the spatial fieldprofile of the remaining eddy fields may not match the spatial fieldprofile of the magnetic field generated by gradient coils 120. Namely,they can have non-linear spatial profiles as shown in FIG. 7.Accordingly, the remaining eddy fields cannot be readily reduced bymodifying the current waveform sent through the gradient coils 120.

Implementing the gradient coils 120 so that they produce constrainededdy fields can enable the use of asymmetric gradient coils 120 foradvanced imaging techniques. In some implementations, constraining ofeddy fields can be achieved on the basis of the gradient coils 120design. For example, the design of the asymmetric and shielded gradientcoils 120 can be implemented such that the remaining eddy fields matchthe spatial profile of the gradient fields (for example, can bespatially linear) generated by the gradient coils 120. Alternatively, orin addition, the design of the gradient coils 120 can enable the eddyfields to be constrained such that they can be actively compensated for.For example, asymmetric gradient coils 120 can be implemented to produceeddy fields that can be represented by the desired set of the gradientcoils 120 and the correction coils 140. For example, constrained eddyfields caused by the gradient coils 120 can be controlled dynamicallythrough the correction coils 140, during the operation of the gradientcoils 120.

There are many ways that the eddy-field metric can be defined. Anexample definition is the sum of the squared difference between theeddy-field that is produced by the gradient coils 120 and the targeteddy-field, which represent the desired constraints on the eddy-field,over a set of points on the volume of a region of interest. Based onthis definition, the eddy-field metric is lowered, to the extentpossible, in light of other performance metric requirements specified.For example, a particular winding pattern can be chosen to obtain aparticular eddy-field metric that may be higher than the lowest possibleeddy-field metric so that specified requirements for other performancemetrics can be met. It is to be understood by those of skill that othersimilar eddy-field metric definitions and minimizations can be used,such as minimizing the eddy-current density over a known conductingsurface.

To achieve the performance metric limits associated with differentperformance metric requirements, a representation of the current densityfor the gradient coils 120 over the surface where the gradient coils 120are to reside (for example, a cylinder) can be generated. Thisrepresentation can be analytic, usually incorporating some sort of basisrepresentation for the given geometry. For example, where the gradientcoils 120 are to reside on a cylinder, cylindrical harmonics can be usedas the basis representation. Alternatively, the representation can benumerical. For example, the current density for the gradient coils 120can be based on current elements over a finite triangular mesh. In aboundary element method (BEM) approach to coil design, for example, anysurface on which electrical current can flow can be approximated orrepresented by a collection of triangular elements that form a mesh overthe whole surface. Within each element is contained information thatdescribes the direction and magnitude of the electrical current density.A step in the BEM, accordingly, is the discretization of a surfacegeometry into a finite mesh composed of triangular elements. Thetriangular elements are hereinafter referred to as elements and thevertices of these elements are hereinafter referred to as nodes. FIG. 8shows an example cylindrical surface onto which the gradient coils 120are to be placed, discretized into a fine mesh composed of triangles.

In practice, in accordance with the BEM, the current density patternover a two dimensional surface can be represented in an indirect mannerin the form of a scalar stream function. The stream function can berepresented as a piece-wise linear (or higher order) function over thesurface geometry on which the gradient coils 120 are to be placed. Thestream function can consist of a single scalar value for each node inthe mesh and when all of the nodes are considered together, the streamfunction can be transformed to find the direction and magnitude of thecurrent density in each triangular element.

In one implementation, a stream function, ψ(r), residing within thesurface of elements with corresponding current density J(r) can bedefined, where r represents the position on the mesh. The streamfunction can be approximated by a weighted sum of basis functions foreach node n as:

$\begin{matrix}{{\psi(r)} = {\sum\limits_{n = 1}^{N}{I_{n}{\psi_{n}(r)}}}} & \left( {{equation}\mspace{14mu} 1.1} \right)\end{matrix}$

In equation 1.1, I_(n) is the weighting coefficient for the basisfunction ψ_(n)(r) of node n. With this approximation, the currentdensity for the stream function can be represented as a sum of currentdensity basis functions, defined as:

$\begin{matrix}{{J(r)} = {\nabla{\times \left\lbrack {{\psi(r)}{n(r)}} \right\rbrack}}} & \left( {{equation}\mspace{14mu} 1.2} \right) \\{{J(r)} \approx {\sum\limits_{n = 1}^{N}{I_{n}{\nabla{\times \left\lbrack {{\psi_{n}(r)}{n(r)}} \right\rbrack}}}}} & \left( {{equation}\mspace{14mu} 1.3} \right) \\{{J(r)} \approx {\sum\limits_{n = 1}^{N}{I_{n}{J_{n}(r)}}}} & \left( {{equation}\mspace{14mu} 1.4} \right) \\{{{J_{n}(r)} \approx {\sum\limits_{k = 1}^{K}v_{nk}}} = {\sum\limits_{k = 1}^{K}\frac{e_{nk}}{2A_{k}}}} & \left( {{equation}\mspace{14mu} 1.5} \right)\end{matrix}$

In equations 1.2 through 1.5, n(r) is the outward pointing normal of thesurface, K is the number of triangles surrounding node n, A_(k) is thearea of triangular element k associated with node n, and e_(nk) is thevector that opposes node n within triangular element k.

The current density representation (or the stream functions) can be usedto produce a pattern of current density that achieves the setrequirements for performance metrics such as balancing of matchingmagnetic field targets and having low power dissipation while at thesame time satisfying specified requirements for eddy currents. Forexample, performance metrics that can be described by a current density,including for example, the gradient field-shape metric, dissipativepower, energy, eddy currents, force and torque can be described based onvarious performance metric functions.

To find the stream function and corresponding current densityrepresentation that achieves the specified requirements set forperformance metrics, a performance functional can be formed using theperformance metrics as functions. In some implementations, theperformance metric functions can include weighting parameters. In otherimplementations, performance metric functions may be set as constraintson the performance functional. A constraint can be set in the form of asingle value (i.e. constrained to zero) or a range of values that areacceptable for that performance function. In yet further variations, theabove discussed approaches to satisfying the performance metricrequirements may be combined, for example some performance metrics beingused to constrain the performance functional and other performancemetrics including weighting parameters.

As an example of using constraints, in some implementations, the streamfunction for a given surface can conjointly be broken down into alinearly independent basis set of stream function modes (calledeigenmodes, or just modes). Higher order modes are represented by streamfunctions that have a greater degree of spatial variation over shorterdistances. For example, the modes can represent orthogonal spatial fieldvariations that correspond to spherical harmonic field variations. Thetotal stream function is then represented as a linear combination ofmodes. As an example, the stream function corresponding to the eddycurrent density induced on a conducting surface, such as the bore of themain field magnet 110, can be represented by a linear combination ofmodes. The eddy current stream function can be calculated through themutual inductance of the calculated current density of the gradientcoils 120 representation with the conducting surfaces of interest, suchas the main magnet 110's bore.

To constrain the induced eddy currents to take on a particular magneticfield shape (for example, allowing only a mode that produces an eddyfield that closely matches the spatial variation of the gradient field),a set of modes other than the desired modes (for example, higher orderspherical harmonic modes) can be suppressed. The suppression can beachieved by including in the performance metric functional a constraintthat the amplitude of any undesired modes be suppressed to a minimalvalue or zero. Accordingly, the eddy field components that cannot becompensated for can thus be eliminated. For example, for cylindricalasymmetric gradient coils, it may not be necessary to includeconstraints for modes that produce field variation of a higher orderthan approximately the 4th order in the spherical harmonic basis becausethe spatial variation of a normal gradient wire pattern does nottypically change rapidly over short distances. For non-cylindricalgradient coils, it may be necessary to suppress higher order modes thanfor the cylindrical case. As a further example, when the MRI system 100includes second order correction coils 140, third and higher order modescan be suppressed, thus enabling the shim coils 140 to compensate forthe resulting eddy fields. In variations, the modes can be weighted toobtain eddy fields with desired shapes. Accordingly, any combination ofzeroth, first or higher-order modes, combined in a weighted manner canbe formed.

Once the performance functional is formed, it can be minimized oroptimized to produce a current density pattern that achieves thespecified gradient coil performance metric constraints. The minimizationcan be based on various techniques such as least-squares matrixinversion, analytic formulae or an iterative solver. For example, whereone or more performance metric functions include weighting parameters,the competing performance metrics can be balanced simultaneously, toachieve the desired performance metric requirements such as low powerdissipation and desired field shape by finding a set of parameters thatminimizes the performance functional. As a further example, inimplementations where one or more performance metrics are set asconstrains, constrained optimization can be used to find the desiredperformance metric requirements. In variations, the solution of theperformance functional itself can be set to be constrained to a certaindesired range. If not in range, performance metrics or weightingparameters can be changed, for example, to obtain a different solution.This process can be repeated iteratively until the obtained solution iswithin the range of acceptable design goals. Example goals includeminimum conductor separation, maximum power deposition per unit area,maximum force on a given component and others.

The resulting current density pattern obtained by minimizing oroptimizing the performance functional can be contoured to obtain a wirepattern, which is a discrete number of current paths that approximatesthe current density represented by the stream function. FIGS. 9(a) and9(b) displays a stream function and corresponding wire patternrespectively after contouring for a transverse gradient coil implementedover a cylindrical surface. The choice of number of contours (and thusthe coil wire density) can also be based on the performance metricweightings and constraints since some of the performance metricweightings and constraints may be related to wire density, for example,a constraint to enforce a certain minimum wire separation.

Using the gradient coil implementation method allows any desired surfaceshape to be used over which the coil can be implemented. Thediscretization of the stream function is dependent on the shape of thefinite elements making up the mesh rather than the shape of the finalsurface. However, the mesh surfaces are typically non-intersecting.

Referring to FIG. 10 a method of manufacturing gradient coils 120 isshown at 1000. At 1010, a volume of interest where the gradient fieldwill be generated is chosen. This typically corresponds to a volumewithin the main magnet 110. At 1020, eddy field causing structuresurfaces are identified, which in this example is the bore of the mainmagnet 110. At 1030, the shape of the surface on which the gradientcoils 120 are to be placed are identified, which in this example is acylinder within the bore of the main magnet 110. At 1040,representations of the surfaces are formed. For example, the surface andcylindrical surface are triangulated and representations formed. At 1050performance metric set limits are identified, in this example in theform of constraints. Specifically, in this example, the two constraintsare the gradient linearity metric and the eddy field metric. The targeteddy-fields have the modes that produce field variations higher thansecond order spherical harmonics suppressed since the correction coils140 are second order coils and cannot correct for modes higher thansecond order spherical harmonics. At 1060 a performance functional isformed and minimized. The performance functional in this exampleincludes performance metric functions for the gradient linearity metricand the eddy-field metric. At 1070 the current density is computed basedon the minimized performance functional and coil windings are obtainedbased on a contouring of the current density pattern.

In variations, the manufactured gradient coils 120 can be operated insuch a manner so as to include compensation currents through thegradient coils 120 and correction coils 140 to cancel the eddy fieldsproduced. The compensation currents can be determined by prospectivelysimulating and determining on the basis of the simulation the eddycurrent response for any pulse sequence. The simulated eddy-fieldprofile can then be decomposed into a linear combination of the fieldsproduced by the correction coils 140 at each time step such that thecombination of currents through the gradient coils 120 and correctioncoils 140 produce a magnetic field in the imaging volume that cancelsthe eddy field to the extent possible. This can be achieved through, forexample, a least-squares minimization or any other similar method. Analternative method is to measure the time and spatial variations of eddycurrents for a pulse sequence and then compute the best fit electricalcurrent waveform to pass through the correction coils 140 forcompensation. The required correction current waveforms can be savedwith the pulse sequence for example at the data processing system 105and played out at the same time as the pulse sequence gradient waveformsto provide the necessary real-time compensation.

The gradient coils 120 manufactured and operated in accordance with theabove described methods can be applied to any application or geometry ofMRI systems. For example, in one variation the imaging region may be atthe center of the gradient coils 120 and the conducting surfaces in theMRI environment may not be distributed symmetrically around the gradientcoil. When the positions of the conducting surfaces are fixed and known,the gradient coil implementation method can be adjusted to produce eddycurrents constrained in order to facilitate dynamic correction.

In variations, the above discussed methods can also be applied to thedesign, manufacture and operation of electromagnets besides gradientcoils. For example, the main magnet 105 or correction coils 140 can alsobe manufactured in accordance with the above described processes. As afurther example, field-shifting coils used in delta relaxation enhancedmagnetic resonance imaging can also be designed, manufactured andoperated in accordance with the above described processes.

The above-described embodiments are intended to be examples andalterations and modifications may be effected thereto, by those of skillin the art, without departing from the scope which is defined solely bythe claims appended hereto. For example, methods, systems andembodiments discussed can be varied and combined, in full or in part.

We claim:
 1. A method of manufacturing electromagnet coils for use in amagnetic resonance imaging (MM) system, the method comprising: forming acoil representation of a coil surface for the electromagnet coils;setting a plurality of performance metric requirements for a pluralityof performance metrics for the electromagnet coils, the plurality ofperformance metrics including a magnetic field-shape metric and aneddy-field metric; forming a performance functional, based on the coilrepresentation and the plurality of performance metrics, for generatinga current density pattern over the coil surface; optimizing theperformance functional based on the plurality of performance metricrequirements; generating a current density pattern over the coil surfacebased on the minimized performance functional; obtaining coil windingsfrom the current density pattern; wherein the MM system furthercomprises correction coils; wherein the eddy-field metric is apredetermined eddy field shape; wherein optimizing the performancefunctional further comprises constraining an eddy current densityrepresentation over an eddy-field producing structure surface such thateddy fields predicted by the eddy-current density representation conformto said predetermined eddy field shape; and obtaining further coilwindings for said correction coils from said eddy-current densityrepresentation thereby enabling the correction coils to compensate forsaid eddy fields.
 2. The method of claim 1 wherein said correction coilsare second order correction coils and wherein the eddy current densityrepresentation is constrained by suppressing third and higher ordermodes.
 3. The method of claim 2 further including weighting said higherorders modes for defining said predetermined eddy field shape.
 4. Themethod of claim 1 wherein the eddy-field metric further comprises atarget eddy field shape; and wherein the optimizing of the performancefunctional further comprises minimizing the difference between thetarget eddy field shape and a predicted eddy field generated based onthe performance functional.
 5. The method of claim 1 wherein theoptimizing of the performance functional further comprises minimizing apredicted eddy-current density pattern generated over an eddy-fieldproducing structure surface based on the performance functional.
 6. Themethod of claim 1 wherein the performance metrics can further compriseat least one of: a net force metric, a net torque metric, a dissipativepower metric and an energy metric.
 7. The method of claim 1 furthercomprising: forming a plurality of performance metric functions based onthe plurality of performance metrics, and wherein the performancefunctional is formed from the plurality of performance metric functions.8. The method of claim 1 wherein the coil representation is based on aboundary element method.
 9. The method of claim 1 wherein the coilsurface is cylindrical.
 10. The method of claim 1 wherein the eddy-fieldproducing structure is at least one of a bore of a main magnet and endflanges of a main magnet.
 11. The method of claim 1 further comprising:generating simulated eddy currents based on the optimized performancefunctional; determining compensation currents based on the simulatededdy currents for correcting eddy fields producible by the simulatededdy currents.
 12. The method of claim 11 wherein the electromagnetcoils are gradient coils and the compensation currents are to begenerated by gradient coils during the operation of the MRI.
 13. Themethod of claim 1 wherein the determining further comprises: minimizingthe eddy fields producible by the simulated eddy currents.
 14. Themethod of claim 1 wherein the electromagnet coils are gradient coils andwherein determining further comprises: when the MM is constructed:measuring the time and spatial variations of the eddy currents for apulse sequence; and determining the compensation currents based on themeasured time and spatial variations of the eddy currents for the pulsesequence.
 15. The method of claim 14 further comprising: after thedetermining, storing the compensation currents in association with thepulse sequence.
 16. The method of claim 1 wherein the electromagnetcoils are one of a main magnet, gradient coils and said correctioncoils.
 17. The method of claim 1, wherein said eddy current density isbased on spherical harmonics.
 18. The method of claim 11, wherein saidcompensation currents are generated by shim coils of at least 2^(nd)order.
 19. The method of claim 11, wherein compensation currents aregenerated by compensation coils configured to correct for said predictededdy fields.
 20. The method of claim 1, wherein said compensation coilsare designed based on one of either measured or simulated eddy currents.21. An MM system manufactured in accordance with the method of claim 1.